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  4. The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will

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Q. The radius of curvature of the curved surface of a plano-convex lens is $20\, cm$. If the refractive index of the material of the lens be $1.5$, it will

Ray Optics and Optical Instruments

Solution:

Here, $\mu = 1.5$
If object lies on plane side;
$R_1 = \infty , R_2 = - 20 \,cm$
image
$\frac{1}{f} = \left(\mu -1\right)\left(\frac{1}{R_{1}} -\frac{1}{R_{2}}\right) $
$= \left(1.5 -1\right)\left(\frac{1}{\infty} + \frac{1}{20}\right) = \frac{1}{40}$
$f = + 40 \,cm$. The lens behaves as convex lens.
If object lies on its curved side. Then
$R_1 = 20 \,cm, R_2 = \infty$
image
$\frac{1}{f'} = \left(\mu -1\right)\left(\frac{1}{R_{1}} -\frac{1}{R_{2}}\right) $
$ = \left(1.5 -1\right)\left(\frac{1}{20} - \frac{1}{\infty}\right) = \frac{1}{40}$
$f'= 40 \,cm$.
The lens behaves as convex lens.